The word "Asteroid" drives me nuts because it's used for everything in Sins. I wish they'd called it "PLANETOID" for the colonizable asteroid, and ASTEROID for the mineable ones.
Here's a synopsis that might help.
COLONIZABLE PLANETS include the four types of world (terran, desert, volcanic, ice) plus COLONIZABLE ASTEROIDS. Of the last, there are two types - ASTEROIDS and DEAD ASTEROIDS. ASTEROIDS support a population with one upgrade (10 --> 20 people), and always have two or more RESOURCE ASTEROIDS in their gravity well that you can construct mines on. DEAD ASTEROIDS are also colonizable, but come with zero population and no RESOURCE ASTEROIDS. The only reason you'd colonize a DEAD ASTEROID(because it generates zero taxes and has zero logistics slots) is that you can build military structures around it like hangars, regen bays and turrets so it can be used as a chokepoint defense.
Of RESOURCE ASTEROIDS, there are two basic types - PLANETARY ASTEROIDS that only are found in all colonizable world gravity-wells except DEAD ASTEROIDS, and indestructible ASTEROID MINES that are independent and found in gravity wells that do not have colonizable bodies (like space wrecks). After you colonize the planet, you can build crystal and metal mines on the former; you use scouts (vasari) or colony ships (advent; TEC) to take over the latter so their production gets added to your queue.
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Construction ships are autogenerated every so often. If one gets destroyed, another will eventually magically appear as long as you own the planet.
-- Retro